An initial optical design method based on an iterative calculation of third-order aberration is presented to overcome the problems of the conventional method. The aberrations of each lens group in the optical system are calculated individually and iteratively under the constraint that aberrations of one group compensate for those of the other groups. The stabilities of initial design results have been confirmed and the iterative design method has been applied for the design of optical system with an external entrance pupil for imaging spectrometer. The designed lens corresponds to an objective lens with the aperture of F/1.5 and the focal length of 30 mm.